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4-1.Complex numbers
normal
If $z_1 = 1+2i$ and $z_2 = 3+5i$ , then ${\mathop{\rm Re}\nolimits} \,\left( {\frac{{{{\overline Z }_2}{Z_1}}}{{{Z_2}}}} \right) = $
A
$\frac {-31}{17}$
B
$\frac {17}{22}$
C
$\frac {-17}{31}$
D
$\frac {22}{17}$
Solution
Given, $z_{1}=1+2 i, z_{2}=3+5 i$ and $\bar{z}_{2}=3-5 i$
$\frac{\bar{z}_{2} z_{1}}{z_{2}}=\frac{(3-5 i)(1+2 i)}{(3+5 i)}=\frac{13+i}{3+5 i}$
$=\frac{13+i}{3+5 i} \times \frac{3-5 i}{3-5 i}=\frac{44-62 i}{34}$
Then $\operatorname{Re}\left(\frac{\bar{z}_{2} z_{1}}{z_{2}}\right)=\frac{44}{34}=\frac{22}{17}$
Standard 11
Mathematics
